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Journal of Operator Theory

Volume 70, Issue 1, Summer 2013  pp. 165-174.

A Birkhoff type transitivity theorem for non-separable completely metrizable spaces with applications to linear dynamics

Authors Antonios Manoussos
Author institution: Fakultaet fuer Mathematik, SFB 701, Universitaet Bielefeld, Postfach 100\-131, D-33501 Bielefeld, Germany

Summary:  In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Frechet spaces. Among them we show that any positive power and any unimodular multiple of a topologically transitive linear operator is topologically transitive, generalizing similar results of S.I. Ansari and F. Leon-Saavedra -- V. Muller for hypercyclic operators.

Keywords:  Topological transitivity, hypercyclicity, Birkhoff's transitivity theorem, $J$-set, almost topological transitivity

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